Measure to Measure
Challenge Problems1. What cut size would we need to have a box with a volume of 700 units3?
The cut should be either 2.5 units or about 4.75 units. Use the blue slider to
read off of the volume curve. Note that there are two possible answers, which
is typical of quadratic (parabola shaped) relationships
2. A box can hold 1.00 kg of sand. What is the box's approximate volume?
The volume in the example would be around 555.56 units3.
(Mass / Density = 1.0 / .0018). Your values will depend on actual sand
density. but should be approximately 300-700 units.
3. If we make a box with a cut of 9.5 units, how many kg of sand could this box hold?
There would be no box! The volume and mass would therefore be 0.
4. A box has a volume of 400 units3, what is its surface area?
The surface area would be approximatly 471 units2 or
284 units2 . Again, there are two answers - Use the volume
curve to find the corresponding cut and then put the cut values into the
surface area formula.
5. We want a box to hold 0.5 kg of sand, what should our cut be?
With a density of .0018, either around 0.65 units or 7.65 units.
Will vary based on densities, but
divide mass by density to get volume, then determine cut from the volume
function.